You have to pick a pizza with 1 crust, 3 toppings and 1 cheese. You have 3 crust options, 7 topping options and 3 cheese options. How many choices do I have?

Question

You have to pick a pizza with 1 crust, 3 toppings and 1 cheese.  

You have 3 crust options, 7 topping options and 3 cheese options.

How many combinations options do I have?

Answer 1

It should be pretty obvious that you have 3 choices for the crust and 3 choices for the cheese, so you have a total of 3*3 = 9 choices for these 2 parts of the pizza.  

 

The number of ways to choose 3 toppings from 7 options is given by ₇C₃, which is read "7 choose 3".  If you don't know what this symbol means, or why it's the appropriate formula for this kind of problem, you should talk to your teacher or one of your classmates or meet with a tutor in person.  The explanation is not particularly complicated but it is somewhat lengthy to type out.  

 

Once you have calculated ₇C₃ you can simply multiply that number by the 3 crust choices and the 3 cheese choices to determine the total number of options.  

 

By the way, the discussion of ₇C₃ in the 2nd paragraph above assumes that no topping can be repeated in the 3 choices.  If a topping can be repeated (for example, if one of your choices of 3 toppings could be pepperoni, more pepperoni, and even more pepperoni) then the number of ways to pick 3 toppings from 7 options would be different.  Can you figure out what it would be?